Compositionality and Coercion in Semantics: The Dynamics of Adjective Meaning
Compositionality and Coercion in Semantics: The Dynamics of Adjective Meaning
Compositionality and Coercion in Semantics: The Dynamics of Adjective Meaning
Partee
Abstract
The focus of the paper will be some aspects of the interaction of meaning and con-
text with different kinds of adjectives. Adjective meanings are shown to be more con-
strained than was appreciated in earlier work. Facts about “NP-splitting” in Polish cast
serious doubt on the standard hierarchy of adjectives, and the data become much more
orderly if privative adjectives are reanalyzed as subsective adjectives. This revised ac-
count requires the possibility of coerced expansion of the denotation of the noun to
which an adjective is applied. Compositionality can be seen as one of the driving forces
in such context-sensitive meaning shifts.
0 Introduction
Starting from some widely shared common-sense ideas about meanings, we will show
how some general methodological strategies can lead to the conclusion that at least one
central ingredient of the meaning of a sentence must be a specification of the condi-
tions under which it is true, and therefore that one central ingredient of word meanings
must be their contribution to the truth-conditions of sentences. Truth conditions give
both more and less information than the actual truth value of a sentence; more, because
they specify truth values in all possible worlds, i.e., they tell what a state of affairs must
be like for the given sentence to be true in it; but also less, because we may know the
truth conditions without knowing which kind of world the actual world is. The kind of
framework this leads to is known variously (with further differences on which we will
1 I am grateful to Anita Nowak for acquainting me with the Polish Split-NP facts, and to Meredith
Landman for initial stimulating discussion. For valuable comments and discussion I am grateful to Lisa
Matthewson and the participants in her UMass. Fall 2000 Pro-Seminar on Modifiers, to several classes
of students at RGGU in Moscow, to participants of a colloquium in honor of Terry Parsons at Notre
Dame in 2003, and to audiences in Leipzig, Copenhagen, Amsterdam, Arizona, and Prague. I thank
Maria Gouskova, Bozena Cetnarowska, and Bozena Rozwadowska for very helpful discussions of the
data. This paper overlaps considerably with Partee (in press). This material is based on work supported
by the National Science Foundation under Grants No. BCS-9905748 and BCS-0418311 to Barbara Partee
and Vladimir Borschev.
We will sharpen this principle further below, but this is a good if informal statement
of the basic principle. There have been many challenges to it of different sorts; my
own view is that (a) there are so many other variables in linguistic theories that it can
hardly be a straightforwardly empirical claim, but (b) it makes a good working princi-
ple: apparent counterexamples are invitations to work hard to uncover new descriptive
accounts or to make revisions somewhere in the theoretical framework.
The focus of the paper will be some aspects of the dynamic interaction of meaning
and context. One important challenge faced by compositional approaches such as for-
mal semantics is how to account for context-dependent meaning shifts without aban-
doning compositionality. We argue here that in fact compositionality can be seen as
one of the driving forces in context-sensitive meaning shifts. Our case study will be
the semantics of different kinds of adjectives. The interplay of context-dependence and
intensionality will be illustrated in showing why skillful is intensional but large is not,
even though we may consider a large house not to be a large building. We will also
take up the puzzles of “privative” adjectives like fake and counterfeit and “redundant”
adjectives like real. The perspective we will take is how attention to the semantics of
syntactic structure (compositional semantics) sheds light on the word meaning, and
how compositional semantics, lexical semantics, and the context of the utterance all
interact. One of the broader implications of this perspective is that there should in
principle be no conflict between the goals of “formal” and “cognitive” approaches to
semantics, although there are of course differences in priorities and in favored forms of
argumentation.
We stated above that a central principle of formal semantics is that the relation between
syntax and semantics is compositional:
Each of the key terms in the principle is a “theory-dependent” term, and there are as
many versions of the principle as there are ways of specifying those terms (meaning,
function, parts (syntax)). See Partee (1984).
Earlier linguistic tradition: 1960s. Katz and Fodor argued for compositional semantics
(“projections principles”), but with meanings as (uninterpreted) “semantic represen-
tations” in the form of bundles of “semantic features”; criteria of correctness are
unclear. The emphasis is on accounting for ambiguity (deriving more than one se-
mantic representation), anomaly (zero SR’s), and some kinds of semantic related-
ness.
The logic tradition: Frege, Tarski, Carnap, Montague. The basic meaning of a sen-
tence is its truth-conditions: to know the meaning of a sentence is to know what
the world must be like if the sentence is true. There are basic criteria of adequacy:
get the truth-conditions and entailment relations right. This tradition was introduced
into linguistics in the 1970s (as “Montague grammar”) and gradually became the
dominant approach to semantics (now “formal semantics”).
The mental representation tradition: Fodor, Jackendoff and others. The basic meaning
of a sentence is a representation in a “language of thought” or “conceptual represen-
tation”. Compositionality is then compositionality of translation.
In the Montague Grammar tradition (Montague, 1970a, 1970b, 1973) the task of a
semantics for language L is to provide truth conditions for every well-formed sentence
of L, and to do so in a compositional way. This task requires providing appropriate
Model structures arise from the way humans schematize situations they want to de-
scribe. When we view a natural language as a formal language, we simultaneously view
the world (or the set of possible worlds) as a model of it. This involves some abstrac-
tion and regimentation both of the language and of the world(s), as reflected in the type
structure imposed on the language and the ontology of the model structures in which
it is interpreted. Ideally, this abstraction should mirror a “real” abstraction which our
“language faculty” imposes on the real world, “natural language metaphysics” (Bach,
1986) or naivnaja kartina mira ‘naive picture of the world’ (Apresjan, 1986).
We consider a sentence or a text as a theory describing the model of the situation
(model of this theory) (Borschev and Partee, 1998). This theory is formed from several
sources:
Whether such meaning postulates are possible for more than a small fraction of the
lexicon of a natural language is a matter of debate.
(iii) Meaning postulates can put constraints on the interrelations that must hold
among the meanings of certain words without necessarily treating one word as “more
basic” than another or decomposing both of them into some common “atoms”. De-
compositional analyses are not forbidden but are not required; that issue can be open to
2 The Moscow school approach to lexical semantics is described in such works as (Apresjan et al., 1969;
Apresjan, 1974, 1992, 1994, 1995, 2000; Mel’chuk, 1974, 1982, 1988; Mel’chuk and Zholkovsky, 1984;
Žolkovsky and Mel’chuk, 1966). We emphasize the Moscow school approach here because one of the
long-term goals of our joint work with our Russian colleagues is a synthesis of compositional and lexical
semantics, particularly Western formal semantics and Moscow-school lexical semantics.
4 Adjective classification
Skillful is not intersective, but it is subsective (Parsons: standard): (6) holds for any N :
The adjectives former, alleged, counterfeit are neither intersective nor subsective:
former senator
= former ∩ senator, (7a)
former senator
⊂ senator. (7b)
The conclusion drawn by Parsons, Kamp, Clark and Montague was that the simplest
general rule for interpretation of the combination of an adjective with a noun (or com-
mon noun phrase: CNP) is the following: Adjectives are functions that map the (inten-
sional) semantic value of the CNP they combine with onto the semantic value of the
ADJ + CNP combination. That is, “The denotation of an adjective phrase is always
a function from properties to properties. (This was one of the proposals advanced by
Kamp and Parsons.)” (Montague, 1970b, 1973, p. 211)
In terms of the type theory of Montague’s Intensional Logic (Montague, 1970a,
1973), where common noun phrases are of type s, e, t, this meant that the most
general type for adjectives was taken to be s, s, e, t, s, e, t. On the variant of
Bennett (1974), followed in most subsequent work in the Montague grammar tradition,
the CNP is of type e, t, and adjectives are then of type s, e, t, e, t.
Meaning postulates specify various restrictions on these functions, characterizing
various subclasses of adjectives. “Semantic features” may be seen as labels for meaning
postulates which give them determinate content. Thus a lexical entry for an intersec-
tive adjective like green might contain the “feature” Intersective, or +I NTERSECTIVE,
which can be taken as labeling a semantic property of the adjective, spelled out by a
meaning postulate.
Meaning postulates for the subtypes listed above are spelled out in somewhat more
formal terms below. The meaning postulates are written with the assumption that the
basic type for all adjectives is s, e, t, e, t.
[Alternatively, intersective adjectives (and only those) can be interpreted in type e, t.
This automatically guarantees their intersectivity and eliminates the need for a meaning
postulate. Type-shifting rules of the sort described in Partee (1995) will give them
homonyms of type e, t, e, t when needed.]
Privative adjectives:
For each privative
∨ adjective meaning ADJ ,
(12)
∀Qs,e,t ∀xe ADJ (Q)(x) → ¬ Q(x) .
The privative adjectives (fake, counterfeit) have a “negative” meaning postulate; a fake
gun is not a gun.
On this familiar classification, adjectives are seen as forming a hierarchy from in-
tersective to subsective to nonsubsective, with the privative adjectives an extreme case
of the nonsubsective adjectives.3
There are of course many questions and disputes when it comes to assigning par-
ticular adjectives to particular classes. Kamp (1975) added an important dimension to
the discussion in arguing that adjectives like tall, which at first sight seem to be non-
intersective, are actually intersective but context-dependent. Kamp’s analysis found lin-
guistic support in Siegel’s analysis of long-form and short-form adjectives in Russian
(Siegel, 1976a, 1976b). There has been much further work on the semantics of adjec-
tives in the intervening years, and the context-dependence of interpretation of adjec-
tives is central in the work of Klein (1980) and most recently of Kennedy (1997).
Among many other debated points, one which has always been troubling, and to
which we will return, is the question of whether an adjective or adjectivally used noun
like fake or toy is really privative. One nagging problem, to which we will return, is the
evident tension between the apparent truth of (13a) and the undeniable well-formedness
and interpretability of (13b).
In Section 4.1 we indicated that the inference pattern (5) was a test of whether an
adjective was intersective. By this test, it looks like vague adjectives like tall and young
are nonintersective:
Premise: Tom is a tall 14-year-old.
Premise: Tom is a basketball player.
(5 )
---------------------------------------
Conclusion: Tom is a tall basketball player. INVALID??
3 Although I believe it has been customary to treat these four classes as forming a kind of a scale, with the
intersective adjectives at one end and the privative adjectives at the other, the meaning postulates do not
actually conform to such a linear scale. With respect to the meaning postulates, one can make a three-class
scale, from intersective (the most restricted) to subsective to unrestricted (not-necessarily-subsective). The
intersective adjectives are a subset of the subsective adjectives, which are in turn a subset of the unrestricted
set, i.e. of the set of all adjectives. The privative adjectives are also a subset of the unrestricted set, but one
which is disjoint from the set of subsective adjectives.
Nowak (2000) studied the phenomenon of “split PPs” and “split NPs” in Polish. [See
also (Gouskova, 2000) for related work on Russian, as well as (Junghanns, 2000;
Mehlhorn, 2000).] Ignoring PPs for simplicity, and ignoring the topic-focus structure
that motivates the splitting, the facts are that an NP consisting of Adj and N in Pol-
ish may be “split”, with either the Adj sentence-initial and the N sentence-final, or
the N sentence-initial and the Adj sentence-final. Sequences of Adj’s can be sentence-
initial; only a single element can be sentence-final. Examples of NP-splits (all actu-
ally PP-splits, which combine properties of NP-splits with constraints on where the
preposition can end up) are given in (14)–(15), with the relevant constituents under-
lined.
Sentences (14b) and (15b) are ‘split’ versions of sentences (14a) and (15a), which
represent the unmarked word order. In (14b) the preposition and adjective are in
sentence-initial position and the bare noun is sentence-final, while in (15b) the preposi-
tion and noun are sentence-initial and the adjective is sentence-final. All examples are
from Nowak (2000).4
What is of particular interest here is that some adjectives can participate in the splitting
construction and some cannot.
Do rozległej weszliśmy doliny.
to large-GEN (we)entered valley-GEN (16a)
‘We entered a large VALLEY’.
Do doliny weszliśmy rozległej
to valley-GEN (we)entered large-GEN (16b)
‘We entered a LARGE valley’.
Another important fact is that the ones that cannot split also cannot occur predicatively.
What is peculiar about this data in the light of the traditional classification outlined
in Section 4 is that the NP-split phenomenon does not apply to a “natural class”. It is
6 Principles of interpretation
The hypothesis I propose is that Nowak’s data tells us that adjectives fake and imag-
inary aren’t actually privative, but subsective, and that no adjectives are actually
privative. In interpreting a question like (13b) or sentences like (20a) and (20b),
I hypothesize that we actually expand the denotation of ‘fur’ to include both fake and
real fur.
I don’t care whether that fur is fake fur or real fur. (20a)
I don’t care whether that fur is fake or real. (20b)
In fact, even in (13a), it is reasonable to suppose that the first occurrence of gun, mod-
ified by fake, is similarly coerced, whereas the second, unmodified, occurrence is not.
Normally, in the absence of a modifier like fake or real, all guns are understood to be
real guns, as is evident when one asks how many guns the law permits each person to
own, for instance. Without the coerced expansion of the denotation of the noun, not
only would fake be privative, but the adjective real would always be redundant.5
Kamp and Partee (1995), in discussing the “recalibration” of adjective interpre-
tations in context, introduced a number of principles, including the following “Non-
Vacuity Principle”.
The Non-Vacuity Principle applies not only to simple predicates but to predicates
formed, for instance, by combination of an adjective and a noun: these should be inter-
preted in such a way that the ADJ + N combination is a non-vacuous predicate.
However, Kamp and Partee (1995) also argued, in part on the basis of clear exam-
ples like (22), that in ADJ + N constructions, one first interprets the noun in the given
context (ignoring the adjective), and then “recalibrates” the adjective as necessary. This
principle is expressed as the “Head Primacy Principle” in (23):
In many cases, the Non-Vacuity Principle and the Head Primacy Principle cooperate
to account for the observed results, including not only the examples in (22), but also
the fact that the truth of (24b) is compatible with a nonredundant use of the modifier
in (24a).
If the Head Primacy Principle is absolute, the proposed shift in the interpretation of
the head noun under coercion by a privative adjective like fake or a “tautologous” ad-
jective like real would be impossible. But there are other examples as well that suggest
that the Head Primacy Principle probably has to be seen as nonabsolute. In particular,
there is a large and productive class of “constitutive material” modifiers that occur in
examples like stone lion, wooden horse, velveteen rabbit, rubber duck. It is evidently
so easy to shift nouns from their literal meaning to a meaning “representation/model
of. . . ” that we hardly notice the shift.7
The perspective of Optimality Theory suggests that we can account for this situation
by saying that the Non-Vacuity Principle outranks the Head Primacy Principle. We
normally try to obey both. But if there is no reasonable way to obey the Non-Vacuity
Principle without shifting the noun outside its normal bounds (as in the case of fake
and real), then it may be shifted in such a way as to make the compound predicate
obey the Non-Vacuity Principle. (Since this is always necessary with privative and
“tautologous” modifiers, there might even be something in their lexical semantics that
particularly indicates the need to shift the head to which they apply.) And if there is an
extremely productive and “easy” shift of the noun that would make it easy to satisfy
the Non-Vacuity Principle, as in the case of the “representations” in wooden horse, etc.,
there too we can override the Head Primacy Principle.
And I would suggest that no adjectives are privative (Partee, in press). “Normal”
adjectives are always subsective, and there should be some ways to identify “modal”
adjectives as a special subclass, such that only they are not necessarily subsective.
6 “In the simplest cases, the effect of the interpretation of a head noun on a given context will be to
restrict the local domain to the positive extension of the head in the given context”. (Kamp and Partee,
1995, p. 161, fn. 23.)
7 In fact, in the literature on prototype theory, one can observe that many of the reported experiments
on judgments of prototypicality are carried out with pictures of objects rather than actual objects, but all
of the language of the experiments and of the discussion of the experiments refers to the corresponding
objects, not to pictures of objects. And normally we don’t even notice; starting with our children and their
picture books, we say things like, “Where’s the doggy? There’s the doggy!”. Presumably no normal parent
would say “Where’s the picture of the doggy? There’s the picture of the doggy!”.
The conclusion from such examples seems to be that whether the extension of a noun
like poet at a given time includes only poets living at that time or both living and dead
poets is highly dependent on the rest of the context, and easily shifts. Similar examples
can easily be multiplied, and there may well be other phenomena that should be looked
at in a similar light. Bennett (1974) observed that Montague’s list of intensional verbs
contained verbs of two different sorts. The typical intensional verb in Montague’s list
was seek, which exhibits all the classic opacity properties. But Montague’s list also
included worship and remember, and Bennett noted that an indefinite object with those
verbs is always interpreted as “specific”, not “nonspecific”; the only sense in which it
is “intensional” is that the object in question need not exist at the world and time of
the worshiping or remembering. It might be fruitful to consider these verbs as ones
which sometimes coerce expansion of the domains in which their direct objects are
interpreted rather than as intensional.
If the hypothesis proposed in this section can be maintained, then the classification
of adjectives would be much more neatly constrained. Adjectives would still be func-
tions from properties to properties in the most general case, but in harmony with the
traditional notion of modifiers, they would normally be constrained to be subsective.
We still need to allow for the ‘modal’ adjectives, which are not so constrained; the
Polish data would provide fuel for a proposal to consider them syntactically as well as
semantically distinct. I have said nothing to help with the problem of how to constrain
the nonsubsective adjectives to just the kinds of ‘modal’ adjectives which actually oc-
cur and not allow random nonsubsective functions: this challenge is raised in Heim
7 Conclusions
The adjective puzzles that I have been discussing were designed to illustrate several
issues. One is the need to study lexical semantics and principles of semantic composi-
tion together; decisions about either may have major repercussions for the other. More
importantly for this context, I have tried to show that while contextually influenced
meaning shifts pose challenges for compositionality, we can see that compositionality
plays an essential role in constraining the kinds of meaning shifts that take place. We
hold the principle of compositionality constant in working out (unconsciously) what
shifts our interlocutors may be signaling. In the extreme case we (like children) depend
on compositionality to figure out the meanings of novel words: if we can use contextual
clues to guess what the whole sentence means, we can then “solve” for the meaning
of the unknown word. Compositionality thus appears to be one of the most cognitively
basic principles in the realm of semantics. While many of the most important founda-
tional questions in the field remain open, I believe that the principle of compositionality
has shown its value as a central working hypothesis guiding semantic research.
References
Apresjan, Jurij D., Igor’ Mel’chuk and Aleksandr Zholkovsky. 1969. Semantics and lexicography: To-
wards a new type of unilingual dictionary. In Ferenc Kiefer (ed.), Studies in Syntax and Semantics,
pp. 1–33. Reidel, Dordrecht.
Apresjan, Jurij D. 1974. Leksičeskaja Semantika [Lexical Semantics]. Nauka, Moscow.
Apresjan, Jurij D. 1986. Dejksis v leksike i grammatike i naivnaja model’ mira [Deixis in lexicon and
grammar and the naive model of the world]. Semiotika i Informatika 28.
Apresjan, Jurij D. 1992. Lexical Semantics. A Guide to Russian Vocabulary. Karoma Publishers, Ann
Arbor.
Apresjan, Jurij D. 1994. O jazyke tolkovanij i semantičeskix primitivax [On the language of lexical expli-
cations and semantic primitives]. Izvestija Rossiskoj Akademii Nauk, Serija lit. i jazyka 53.
Apresjan, Jurij D. 1995. Izbrannye Trudy, Vol II: Integral’noe Opisanie Jazyka i Sistemnaja Leksikografia
[Integrated Description of Language and Systematic Lexicography]. Škola “Jazyki Russkoj Kultury”,
Moscow.
Apresjan, Jurij D. 2000. Systematic Lexicography, translated by K. Windle. Oxford University Press, Ox-
ford.
Bach, Emmon. 1986. Natural language metaphysics. In R.B. Marcus, G.J.W. Dorn and P. Weingartner
(eds), Logic, Methodology, and Philosophy of Science VII, pp. 573–595. North-Holland, Amsterdam.
Bennett, Michael. 1974. Some extensions of a Montague fragment of English. PhD dissertation, University
of California at Los Angeles, distributed by Indiana University Linguistics Club.
Borschev, Vladimir and Barbara H. Partee. 1998. Formal and lexical semantics and the genitive in negated
existential sentences in Russian. In Ž. Boskovic, S. Franks and W. Snyder (eds), Formal Approaches
to Slavic Linguistics 6: The Connecticut Meeting 1997, pp. 75–96. Michigan Slavic Publications,
Ann Arbor.